%0 Journal Article
%T 保拓扑结构的非刚性医学图像配准方法<br>Topology-Preserving Non-Rigid Medical Image Registration Method
%A 吴霖磊
%J Advances in Applied Mathematics
%P 21-32
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.144136
%X 图像配准在图像处理领域发挥着举足轻重的作用&#65292;尤其是在医学图像处理领域&#65292;需要能保持原器官拓扑结构的非刚性图像配准方法。本文基于类Beltrami系数的保拓扑结构的非刚性医学图像配准方法&#65292;提出了新的惩罚函数&#65292;使得类Beltrami系数满足<math xmlns='http://www.w3.org/1998/Math/MathML'>
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&#65292;能更好地保证配准过程中的拓扑结构的保持。同时&#65292;我们提出了新的保拓扑结构的非刚性医学图像配准模型&#65292;并证明了关键数学性质。最后&#65292;我们在多个复杂的实际场景中进行了大量实验&#65292;验证了我们方法的优越性。<br>Image registration plays a crucial role in the field of image processing. Particularly in the area of medical image processing, there is a need for non-rigid image registration methods that can preserve the topological structure of original organs. This paper presents a novel penalty function based on the topological-structure-preserving non-rigid medical image registration method using the Beltrami-like coefficients. By using this penalty function, the Beltrami-like coefficients satisfy the condition <math xmlns='http://www.w3.org/1998/Math/MathML'>
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, which can better ensure the preservation of the topological structure during the registration process. Meanwhile, we propose a new topological-structure-preserving non-rigid medical image registration model and prove its key mathematical properties. Finally, we conduct numerous experiments in multiple complex real-world scenarios to verify the superiority of our method.
%K 保拓扑结构&#65292
%K 非刚性&#65292
%K 三维医学图像配准&#65292
%K 变分模型<br>Topology-Preserving
%K Non-Rigid
%K 3D Image Registration
%K Variation Model
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=110803